Munich Personal RePEc Archive

A Supermultiplier Stock-Flow Consistent

model: the return of the paradoxes of

thrift and costs in the long run?

Brochier, Lidia and Macedo e Silva, Antonio Carlos

University of Campinas

21 March 2017

Online at https://mpra.ub.uni-muenchen.de/92673/

MPRA Paper No. 92673, posted 21 Mar 2019 09:38 UTC

A Supermultiplier Stock-Flow Consistent model: the “return”

of the paradoxes of thrift and costs in the long run?

[This version: March 21st, 2017]

Lıdia Brochier⋆

Antonio Carlos Macedo e Silva ⋄

Abstract

Supermultiplier models have been recently brought to the post-Keynesian debate. Yet these modelsstill rely on quite simple economic assumptions, being mostly flow models which omit the financialdeterminants of autonomous expenditures. Since the output growth rate converges in the long run to theexogenously given growth rate of “non-capacity creating” autonomous expenditure and the utilizationrate moves towards the normal utilization rate, the paradoxes of thrift and costs remain valid only as leveleffects (average growth rates). This paper investigates whether the core conclusions of supermultipliermodels hold in a more complex economic framework, described by means of a supermultiplier SFCmodel, in which private business investment is assumed to be completely induced by income while theautonomous expenditure component - in this case consumption out of wealth - becomes endogenous. Theresults of the numerical simulation experiments suggest that the paradox of thrift can remain valid interms of growth effects and that a lower profit share can also be associated to a higher accumulation rate,though with a lower profit rate.

Keywords: Supermultiplier; SFC model; autonomous expenditures; paradoxes of thrift andcosts; growth theories.JEL classification codes: B59, E11, E12, E25, O41.

1 Introduction

Supermultiplier models, as conceived by Sraffian authors (Serrano, 1995a; Bortis,

1997), keep the “Keynesian hypothesis” (Lavoie, 2014, 359), emphasizing the idea that

growth can be demand-led even in the long run. This is made possible through the

introduction of a “non capacity creating” autonomous expenditure which grows at an

⋆Ph.D. Student at the University of Campinas, Brazil. E-mail address: lidiabrochier@gmail.com⋄Associate Professor at the University of Campinas, Brazil. E-mail address: macedo@eco.unicamp.br

1

exogenously given rate and towards which capital accumulation rate will converge in the

long run, as business investment is completely induced by income. One of the consequences

of these assumptions is that, since both capital accumulation and utilization rates converge

to given exogenous values, the paradox of thrift and the paradox of costs are no longer

valid in terms of growth effects in the long run, but only in short and medium runs.

That is to say growth rates can be higher during the traverse period, but not in the fully

adjusted position of the system, when utilization rates reach the normal level.

Supermultiplier models have been recently brought to the post-Keynesian debate

by Allain (2015b) and Lavoie (2016). Besides, some empirical evidence for its main results

is provided by Girardi and Pariboni (2015). However, these models still do not properly

account for the interactions between financial stocks and flows,which - as we sustain here

- could lead to different results regarding the paradoxes in the long run.

The aim of the paper is to verify whether these key results of the supermultiplier

model – that is, that the paradoxes only hold for level effects in the long run – remain valid

in a more financially complex economic framework with interactions between financial

stocks and flows. To accomplish this we propose to build an Stock Flow Consistent model

keeping the supermultiplier approach essentials – namely, the autonomous expenditure

component, induced business investment and the Harrodian investment behavior through

which firms react to the discrepancies between actual and desired utilization rates. We

adopt a consumption function found in most post-Keynesian models, in which households

consume a proportion of their wages and of their wealth. The consumption out of wealth

is the autonomous expenditure component of this economy and since the dynamics of

household wealth is endogenous to the system, we can say that at least part of the

autonomous expenditure component is also endogenous to the model.1

Besides this introduction, the paper is organized as follows. The second section

of the paper briefly reviews the heterodox growth models literature debate over the uti-

lization rate and the consequences of each model, culminating in the proposal of these

alternative (mainly supermultiplier) growth models. In subsection 2.1, we further discuss

the features and results of the recent supermultiplier models and highlight the lack of

financial complexity, which motivates the building of the model in the third section. In

section 3, we present the framework of the model as well as short and long run equilibrium

conditions. Following this, in the fourth section three numerical simulation experiments

are carried out. The experiments are a reduction in firms’ mark-up (subsection 4.1);

an increase in the propensity to consume out of wages (subsection 4.2); and, finally, an

1Fiebiger and Lavoie (2016) call these expenditures ‘semi-autonomous’ since it would be unrealisticto consider that any of the effective demand components could be fully autonomous in the real world.

2

increase in the autonomous expenditure component (an increase in the propensity to con-

sume out of wealth) (subsection 4.3). Still in this section, we make a general assessment

of the shared results of the shocks (subsection 4.4). Section 5 concludes the paper.

2 Heterodox Demand-led growth models

Heterodox growth theories, as well as the neoclassical model of growth2, have

emerged as an attempt to get around the instability presented by Harrod’s model (Kregel,

1980; White, 2008; Fazzari et al., 2013; Cesaratto, 2015). One of the issues raised by

Harrod (1939) is that the steady growth state of the model is unstable because deviations

of the growth rate of the economy from the “warranted growth rate” will make the path

explode or collapse (Fazzari et al., 2013).

Accordingly, the models based on the Cambridge equation (Kaldor, 1961; Robin-

son, 1962) avoided instability assuming endogenous income distribution, what makes it

possible for the system to reach the exogenously given utilization rate in the long run.

However, in these models, a higher profit share was associated to higher accumulation

and profit rates3, which means that getting around instability had come at the cost of

not reproducing the stylized fact that a higher capital accumulation rate can be accom-

modated through an increase in the utilization rate without changing income distribution

between wages and profits (Cesaratto, 2015).

During the 1980s, some central features of Cambridge models began to be more

fiercely questioned, such as full employment, the endogenous income distribution and the

contradiction between short and long run dynamics 4 (Lavoie, 2014). These controversies

originated the first neo-Kaleckian models, as put forward by Rowthorn (1981), Dutt

(1984) and Amadeo (1986), which extended the effective demand principle to the long

run without assuming full capacity utilization and price mechanisms to bring about the

adjustment between investment and savings (Amadeo, 1987; Skott, 2010; Hein et al.,

2012).

These neo-Kaleckian models considered income distribution to be exogenous, so

changes in the capital accumulation rate would take place through the endogenous capac-

2As we focus on heterodox growth theories, namely theories in which growth is led by demand andin which autonomous components of demand can also play a role in the long run, we do not deal withneoclassical growth theories.

3While a higher propensity to save would reduce them both, in consonance with the paradox of thrift.4Contradiction between short run and long run behavior of the economy refers to the fact that in the

short run quantities change to adjust output to demand, through the endogenous utilization rate, whilein the long run, capacity is at its full level, so prices must change to equal output to demand (Lavoie,2014, p.347-359).

3

ity utilization rate, even in the long run. They came up with two particularly interesting

features at the same time: the paradox of thrift and the paradox of costs. The paradox of

thrift says that an increase in the saving rate 5 would lead to lower capital accumulation,

profit and utilization rates in the new equilibrium. The paradox of costs - in the version

initially presented by Rowthorn (1981) - means that an increase in real wages after a

fall in firms’ mark-up would boost consumption and lead to a higher utilization rate and,

consequently, to higher capacity accumulation and profit rates (Dutt, 2011; Lavoie, 2014).

One could say that the paradoxes that emerge from the canonical neo-Kaleckian model

are dynamic paradoxes or paradoxes in terms of “growth effects”. The initial paradox of

thrift as presented by Keynes (1936) referred to the negative effect of a higher propensity

to save on the level of output. Likewise, the paradox of costs as put forward by Kalecki

(1969) considered only the static effect of a decrease in wages on firms’ level of profit

(Lavoie, 2014).

The neo-Kaleckian approach, despite its predominance among post-Keynesian au-

thors, has been repeatedly criticized for not dealing with the Harrodian instability issue.

The point is: since the utilization rate is endogenous in the long run it could be per-

manently higher or lower than the normal or planned utilization rate. In neo-Kaleckian

models, long run accumulation is ultimately exogenous, so a higher utilization rate does

not affect investment plans and, consequently, firms do not revise the trend growth of

sales even with a persistently higher or lower demand. For authors from other heterodox

strands, as some Sraffians, deviations between actual and normal utilization should fos-

ter changes in growth expectations and in investment decisions, giving rise to Harrodian

instability. 6(Hein et al., 2011, 2012; Lavoie, 2014).

As an alternative to neo-Kaleckian models, Serrano (1995a) and Bortis (1997)

proposed the so-called “Sraffian” supermultiplier model, in which long run growth is

demand-led and capacity utilization converges towards the normal or planned levels, by

means of the adjustment of the marginal propensity to invest of private firms. This is

made possible by the introduction of an autonomous demand component growing at an

exogenously given rate while private business investment is assumed to be induced by

income without losing the Keynesian causality of investment to savings. The full induce-

ment of private business investment addresses the criticism that firms must reevaluate

their expected long run growth rate, when the utilization rate diverges from the normal

one. The approach solves a previously impossible trinity, harmonizing the Keynesian

5Since in most neo-Kaleckian models, as a simplification, workers spend all their income and onlycapitalists save, they usually refer to the saving rate of capitalists.

6“(...) It seems unrealistic to assume that the growth rate of sales expected by firms, which is capturedby the parameter γ in the investment function, stays at the same value forever. Overtime, it should slowlyadjust to past changes in the growth rate of sales (...)” (Nah and Lavoie, 2017, p.14).

4

hypothesis, exogenous income distribution and the long run balance between productive

capacity and the aggregate demand Cesaratto (2015).

The first versions of the supermultiplier model (Serrano, 1995a; Bortis, 1997)

lacked a clear depiction of the endogenous mechanism by means of which the utiliza-

tion rate tends towards its normal rate. However, a Harrodian mechanism through which

the propensity to invest becomes endogenous and changes according to the discrepancy

between the actual utilization and the normal one was included in a recent version of

the supermultiplier by Freitas and Serrano (2015), which means at least a conditional

solution to the Harrod’s knife-edge instability problem (Allain, 2015b; Lavoie, 2016). In

a similar fashion to this latest version, the supermultiplier model was brought to the

post-Keynesian debate, within the neo-Kaleckian framework, by Allain (2015b,a) and by

Lavoie (2016). They both combine a “non-capacity creating” autonomous expenditure

component which grows at an exogenously given rate towards which the rate of capital

accumulation will converge in the long run and the Harrodian adjustment mechanism.

These supermultiplier models bring into the scene a whole new spectrum of demand-

led models, which could enrich the post-Keynesian literature, since in most neo-Kaleckian

models, private business investment is the demand component which leads growth, while

there is no reason why this should always be the case 7. From the canonical version of

the neo-Kaleckian model (Dutt, 2011; Hein et al., 2011) to its most popular variant, the

“post-Kaleckian” (Lavoie, 2014) model of Bhaduri and Marglin (1990), this remains as a

predominant feature. This also applies to the more financially complex stock-flow consis-

tent (SFC from now on) models. To be fair, we can find some models in which government

expenditures assume the leading role of growth, as in chapter 11 of Godley and Lavoie

(2007)’s book. However, to our best knowledge, only recently the implications of different

growth-regimes - as for, instance, consumption-led ones - started to be explored 8.

In the next subsection, we deal with these recent supermultiplier growth models

and how they still need to add some financial complexity to the economic framework to

do justice to the post-Keynesian debate about the roles of money and finance on the

7The recent U.S. experience suggests that consumption, for instance, can autonomously grow in re-lation to current income to a large extent and for a considerable period of time (Guttmann and Plihon,2008; Cynamon and Fazzari, 2008; Barba and Pivetti, 2008; Bibow, 2010; Lavoie, 2014; Allain, 2014).The “funding effect” (see Brown, 2007) of some institutional arrangements put forward by financial in-novation, as well as consumer credit with real estate collateral, are good examples of how consumptioncan grow independently of current income growth. In Fazzari et al. (2013)’s words: “(. . . ) the risingimportance of finance for consumer spending strongly suggests that consumption dynamics could play amuch more important role in demand growth than is the case with the passive income based consumption(. . . ) (Fazzari et al., 2013, p. 19).

8Apart from the balance of payment constrained growth models, in which net exports lead growth.However, these models are too partial: most of them do not even include investment decisions, and werethus excluded from this paper (see Blecker, 2009).

5

Table 1: Balance sheet of Supermultiplier models

Assets Households Firms Goverment⋄∑

1. Fixed Capital +Kf +Kf

2. Equities† +E −E 03. Govt. Bills⋄ +B −B 04. Net worth Vh Vf −B +Kf

Note 1: The papers considered in this table are the following: Allain (2015b,a); Freitas and Serrano(2015); Dutt (2016); Lavoie (2016); Hein (2016); Nah and Lavoie (2017).Note 2: The white cells are part of the models in all papers considered in this table.† Equities are included only in Hein (2016).⋄ Government bills are included only in Dutt (2016) and Hein (2016).

dynamics of capitalism.

2.1 The lack of financial determinants in supermultiplier growth models

According to Lavoie (2010), one of the main reservations of post-Keynesians about

the supermultiplier approach is that it does not include the financial features of the

economy, differently from several neo-Kaleckian models, which in the 1990s begun to link

the financial and real sides of the economy9 (Lavoie, 2006; Dutt, 2011). b. This has not

been significantly altered by recently published papers such as Freitas and Serrano (2015);

Lavoie (2016); Allain (2015a); Dutt (2016); Hein (2016).

So far these supermultiplier growth models rely on quite simple economies in order

to obtain analytical solutions. Most of them have only two or three sectors, firms and

households (investment and consumption) and, more recently, government or the foreign

sector; they typically feature only one kind of real asset (the capital stock) and one kind

of financial asset (government debt), if at all. In tables 1 and 2, in which we present

respectively the balance sheet and the transactions flow matrix of the recent models in

this literature, we can notice they are mainly flow models, not paying enough attention

to the interaction between stocks of financial assets and income flows.

We are aware that increasing complexity and dealing with both the real and the

financial sides of the economy might not have been the goals of these models so far. Yet

the inclusion of financial determinants and the analysis of debt and deficit dynamics is

starting to gain momentum (see Dutt, 2015; 2016 and Hein, 2016). In Allain (2015b)

government expenditures lead growth in the long run, but the government budget deficit

is balanced, so there is neither government debt nor interest payments accruing from

9For more on how neo-Kaleckians include financial issues in their models see Dutt (2011) and on howneo-Kaleckians deal with the impacts of financialization on these models see Hein (2011).

6

Table 2: Transactions flow matrix of Supermultiplier models

Households Firms Government† Foreign sector⋆ ∑

Current Capital

1. Consumption −C +C 02. Investment +I −I 03. Govt. expenditures† +G −G 04. Exports⋆ +X −X 05. Imports⋆ −M +M 06. Wages +W −W 05. Taxes† −T +T 07. Profit +FD −F +FU 08. Interest⋄ +iB −iB 0

9. Subtotal Sh 0 Sf Sg Sex 0

Note 1: The models considered are the same ones of table 1.Note 2: The white cells are part of the models in all papers considered in this table.† The Government sector and government expenditures are included in Allain (2015b,a), Dutt (2016)and Hein (2016). Taxes are included in Allain (2015b); Dutt (2016), but not in Hein (2016).⋆ The foreign sector and exports and imports are included only in Nah and Lavoie (2017).⋄ Interest payments on bills are included only in Dutt (2016) and Hein (2016).

government bills. On the other hand, Dutt (2015, 2016) and Hein (2016) address the

effects of debt dynamics on income inequalities in a system where government plays the

leading role of growth.

Dutt (2016) highlights how the supermultiplier mechanism impacts public debt10:

an increase in the growth rate of autonomous government expenditures leads to a higher

accumulation rate during the transition, which means a reduction in the government

deficit to capital ratio and consequently leads to a reduction in the debt to capital ratio,

due to the increase in income and taxation, reducing the financial needs of the government.

The lower debt to capital ratio also means a reduction in the financial income received

by capitalists as a share of capital, thus reducing income inequality; in turn, Hein (2016)

does not deal with taxation issues,focusing on the ambiguous effect of an increase in the

debt to capital ratio on the pre-tax functional distribution of income: a higher deficit

pushes activity, thus increasing production and income from real activity (reducing the

financial income share). On the other hand, the consequent increase in government debt

to capital ratio increases the financial income share received from interest payments.

In table 3, we exhibit the main features and results of these models. The ultimate

source of growth varies: it is consumption out of credit 11 in Freitas and Serrano (2015),

10Dutt (2016) also shows how debt dynamics changes long run stability conditions - the growth rate ofgovernment expenditure should be lower than the normalized saving rate and higher than the after taxinterest rate for stability to hold.

11Girardi and Pariboni (2015) find some evidence that consumption out of credit bears a close corre-

7

it is the capitalists’ consumption in Lavoie (2016) and government expenditures in Allain

(2015b).In (Allain, 2015a), the author proposes an interesting model in which subsistence

consumption, through a redistributive mechanism between employed and unemployed

workers, works as the autonomous variable growing at the exogenous population growth

rate 12. Most of these models explicitly deal with the Harrodian instability problem, by

means of an adjustment mechanism of the expected trend growth rate of sales or (in

the case of Freitas and Serrano (2015)), of the propensity to invest, which makes the

utilization rate converge to the normal rate. In both adjustment mechanisms presented,

Harrodian instability is needed for the utilization to converge to the normal one, as long

as it is not too strong. Therefore, the adjustment of the expected trend growth rate (or

propensity to invest) by firms must be slow.

Despite conciliating the autonomous expenditure component with some financial

complexity - through government debt dynamics - it is important to stress that neither

Hein (2016) nor Dutt (2016) deeply discuss the Harrodian instability issue. Hein (2016)

assumes that the normal utilization is not precisely defined in a world of uncertainty or

that it adjusts endogenously to the actual utilization rate. Indeed, Hein (2016) keeps

the usual neo-Kaleckian investment function, in which animal spirits is exogenous and

capacity utilization adjusts endogenously to the changes in aggregate demand even in the

long run. Differently, Dutt (2016) considers that firms have rational expectations and

assume that the trend growth rate of sales equals the growth rate of the autonomous

demand component chosen.

As far as we know, a more “complete” stock-flow consistent supermultiplier model,

which deals with Harrodian instability issues and which is concerned with growth dynam-

ics, is still rare. In Dos Santos and Zezza (2008), the authors already suggest that it

could be interesting to study an investment function with a Harrodian mechanism, ac-

cording to which firms would adjust their investment demand to stabilize the capacity

utilization, within an SFC framework. More recently, we can find three papers which

include an investment function of the accelerator type in an SFC framework. Both Bortz

(2014); Leite (2015) provide an investment function which makes investment endogenous

and dependent on income but they rely on the assumption that government expenditures

are completely exogenous, so their dynamics will be closely related to the supermultiplier

models described in this section. Pedrosa and Macedo e Silva (2014) also provides a model

in which investment is endogenous and in which government expenditures are a fraction

lation to the GDP and that GDP growth precedes the increase in household consumption credit. Basedon this, they question whether this variable should be considered autonomous in the long run.

12In this paper, Allain claims to have a solution also to the second of Harrod’s problem since the growthrate in the long run also matches the natural rate of growth.

8

of the capital stock, this means the dynamics of the model is closely related to the one

presented by the model proposed here. However, the purpose of the authors is to analyse

the government debt dynamics, which is not our focus here.

As Freitas and Serrano (2015) acknowledge it, it is essential to focus on the financial

determinants and on the dynamics of the different “non-capacity creating” components of

autonomous demand which could take on the leading role on growth. Allain (2015b) also

suggests that the results of supermultiplier models may vary according to the autonomous

expenditure chosen as the growth engine. Hein (2016) stresses that the insights provided

by his model should be examined and assessed in “(...) more complex models, which might

include taxes and thus the post-tax distribution of income, more complicated investment

functions, explicitly considering the issue of investment finance for example, wealth-based

and debt-based consumption, or a foreign sector” (Hein, 2016, p.20).

However, in the (still too simple) supermultiplier models summarized in table 3,

the choice of the engine of growth seems to be inconsequential. The accumulation rate

will converge to the exogenously given growth rate of the leading variable, whatever it is.

A decrease in the propensity to save, for instance, will increase the level of output but will

not permanently effect the growth rate of the economy, since the capital accumulation

rate will converge towards the exogenously given growth rate of autonomous consumption

or government expenditures. The same applies to the paradox of costs. In the case of

(e.g.) a reduction in the profit share, the level of output and the level of profits will be

higher as a consequence of the increase in household expenditures, but the rate of profits

will be lower since the utilization rate converges to the normal utilization rate. 13 14

As mentioned by Lavoie (2016), although the paradoxes of thrift and costs are lost

as growth effects in supermultiplier models, they still hold if redefined as level effects.

This also means that during the traverse from one steady state to the other, growth rates

change, being higher or lower on average. However, the disappearance of the growth

effects reflects the assumption that “non-capacity creating autonomous expenditures” are

completely exogenous. A different picture may emerge if, by means of a more complete

description of the feedbacks between financial stocks and flows, one allows for a specific

engine of growth to become partially endogenous to the model. This is what we propose

in sections 3 and 4.

13To be fair, in Nah and Lavoie (2017) there are some different short and medium run effects, as thesensitivity of the real exchange rate due to changes in income distribution may give rise to wage orprofit-led regimes (table 3).

14Dejuan (2014) also proposes a supermultiplier model in which net exports lead growth but, differentlyfrom Nah and Lavoie (2017), does not analyze the impacts of the sensitivity of real exchange rates toincome distribution, which could change the short and medium run results of the model.

9

Table 3: Supermultiplier models features and results

Model Y Z Investment behaviorResults of a decrease in s Results of a decrease in π

Y gk, gy,u Y gk, gy,u

Allain (2015b) C + I +G Government expenditures Harrodian instability mechanism Permanent + Transient + Permanent + Transient +Allain (2015a) C + I Subsistence consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient +Dutt (2016) C + I +G Government expenditures Rational expectations Permanent + Transient + Permanent + Transient +Hein (2016) C + I +G Government expenditures Animal spirits, endogenous u Permanent + Transient + Permanent + Transient +Freitas and Serrano (2015) C + I Consumption financed by credit Harrodian instability mechanism Permanent + Transient + Permanent + Transient +Lavoie (2016) C + I Capitalist’s consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient +Nah and Lavoie (2016) C + I +XL Net exports Harrodian instability mechanism Permanent + Transient + Permanent +/- Transient +/-

Legend: Y is for output, Z for the autonomous expenditure component, gk for capital accumulation rate, gy for outuput

growth, u for utilization rate, s for propensity to save and π for the profit share.

3 A Supermultiplier Stock-Flow Consistent model

Based on the brief review of the previous section, we propose to build an SFC

model in which the “non-capacity creating” autonomous expenditure component is the

consumption out of household wealth and in which private business investment is to-

tally induced. Since household wealth is endogenous to the model, it follows that the

autonomous expenditure component is also endogenous.15

In the next subsections we present the framework of the model, the short run

equilibrium condition, the dynamics equations and the long run equilibrium conditions.

3.1 Framework of the model

In the present subsection, we describe our SFC model that attempts to incorporate

some of the Supermultiplier approach features. Table 4 presents the balance sheet of the

four institutional sectors featured: households, firms, government and banks. The model

deals with a pure credit closed economy without inflation (price level is stable and equals

the unity). This is so because introducing a Central Bank and/or inflation would make

the model unnecessarily complex for the initial purpose we have in mind. Of course, we

allow for the price of equity to change in order to account for household capital gains or

losses.

Banks lend to firms and receive deposits from households. As banks do not make

profits, deposits earn the same interest rate of loans granted to firms. Firms sell equities

to households and are not credit constrained, for banks grant all demand for loans. As

prices are held constant, one can assume that a monetary authority determines the real

interest rate, as in Ryoo and Skott (2013). Households in this economy hold three kinds

15While the notion of exogeneity vs. endogeneity to the model can be clearly defined, the notion ofautonomy vs. inducement seems to me somewhat arbitrary. In supermultiplier models, investment is notnecessarily induced by current income. In Cesaratto et al. (2003, p. 42), induced investment is a functionof the “expected average rate of growth of normal effective demand over the life of the investment thatis currently being installed”.

10

Table 4: Balance sheet matrix

Assets Household Firms Banks Government∑

1. Deposits +M −M 02. Loans −L +L 03. Fixed capital +Kf +Kf

4. Equities +pe.E −pe.E 05. Government Bills +B −B 06. Net worth Vh Vf 0 −B +Kf

Table 5: Transactions and Flow of Funds matrix

HouseholdFirms

Banks Government∑

Current Capital

1. Consumption −C +C 02. Investment +I −I 03. Government expenditures +G −G 04. Wages +W −W 05. Taxes −T +T 06. Profit +FD −F +FU 07. Deposits interest +ir.M−1 −ir.M−1 08. Loans interest −ir.L−1 +ir.L−1 09. Bills interest +ir.B−1 −ir.B−1 0

10. Subtotal Sh 0 Sf 0 Sg 0

11. ∆ Deposits −∆M +∆M 012. ∆ Loans +∆L −∆L 013. ∆ Equity −pe.∆E +pe.∆E 014. ∆ Bills −∆B +∆B 015.

∑

0 0 0 0 0 0

of assets. They buy equity from productive firms and bills issued by the government and

hold the rest of their wealth in the form of deposits at banks.

Table 5 shows the transactions between institutional sectors in its first part and

the flow of funds in the second part. At this point we can describe the transactions of

each sector and the behavioral assumptions.

Government issues bills to finance its expenditures that are not covered by taxa-

tion of household income 16. Besides, government bills, firms’ loans and household deposits

yield the same interest rate. Government expenditures are a fraction of aggregate income

at the beginning of the period (equation 2) 17. In equation 1, which shows how government

16As in Le Heron and Mouakil (2008) the government only taxes household (not firms) income.17Since many countries pursue austerity measures and we are not focusing on fiscal policy, considering

government expenditures as procyclical should not be a problem, as in Le Heron and Mouakil (2008).

11

debt evolves over time, ir is the real rate of interest, G is the government expenditure, T

is the taxation of household income and B−1 is the stock of bills issued by the government

and held by households at the beginning of the period. In equations 2 and 3 respectively

σ represents the ratio of government expenditures to past income 18 and τ represents the

ratio of taxes on household income.

B = B−1 +G− T + ir.B−1 (1)

G = σ.Y−1 (2)

T = τ.Yh (3)

Household income comprehends wages and financial income (interest on deposits

and bills and dividends) (equation 4). The wage share of income is defined by equa-

tion 5, in which π is firms’ profit share. Household disposable income is defined as the

after-tax household income (equation 6). Households consume a fraction (α1) of their

after-tax wages and a fraction (α2) of their stock of wealth at the beginning of the pe-

riod (equation 7), as in Dos Santos and Zezza (2008). Consumption out of wealth (i.e.

“capitalist consumption”) represents the autonomous expenditure component. Despite

being autonomous (in relation to current income), it is endogenous to the model, since it

depends on household wealth, so we can analyse its dynamics through household wealth

dynamics. Household savings are defined by equation 8. In the model, financial income

does not affect consumption directly, but through its effect on wealth.

Yh = W + FD + ir.(B−1 +M−1) (4)

W = (1− π).Y (5)

Yd = (1− τ).Yh (6)

C = α1(1− τ).W + α2Vh−1 (7)

Sh = Yd − C (8)

Following Dos Santos and Zezza (2008), we suppose that the proportion of household

18Since we are building the model in a discrete time framework, one may wonder whether the stabilityof the model would depend on the lagged effect of income on government expenditures. We have testedthe model for government expenditures based on current income (results can be provided upon request)and the changes we observe, would also be observed in theoretical analytical models. If governmentexpenditures depended on current income, the short run effects of the supermultiplier on the model wouldbe amplified. This means the model would present a higher growth rate, requiring a slower adjustmentof the trend growth of sales or the propensity to invest to keep instability away. This is the same effectobserved in the models of Allain (2015a); Lavoie (2016); Freitas and Serrano (2015).

12

wealth allocated in equities (λ) depends positively on the expectation of return (λ0) and

negatively on the real interest rate (equation 9). The stock of equities issued is decided by

firms. As households buy all equities issued by firms, the price of equities (pe) come into

play to clear the market (equation 10). To avoid indetermination, since bills and deposits

have the same remuneration rate, we suppose that households buy all government bills

(Ryoo and Skott, 2013; Pedrosa and Macedo e Silva, 2014).

λ = λ0 − ir (9)

pe =λ.Vh

E(10)

The stock of wealth changes due to household savings and due to capital gains (equation

11). As households are assumed to buy all bills issued by the government, deposits share

in wealth must be treated as a residual (equation 12)

Vh = Vh−1 + Sh +∆pe.E−1 (11)

M = M−1 + Sh − pe.∆E −∆B (12)

Firms decide the mark-up (µ) on wage costs. The mark-up on costs defines functional

income distribution (Lavoie and Godley, 2001), as in traditional neo-Kaleckian models

(equation 13). Firms must also make their investment decisions and this is where the

supermultiplier approach comes properly into the scene. Aggregate investment of firms

is induced by output (equation 14) (Serrano, 1995a; Freitas and Serrano, 2015). Firms

as a whole have a marginal propensity to invest out of income (h), which is endogenous

to the model and reacts to discrepancies between the utilization rate (u) and the normal

utilization rate (un) (equation 15), following a Harrodian adjustment mechanism (see

Lavoie, 2016; Freitas and Serrano, 2015), in which γ represents the speed of adjustment

of the propensity to invest to the discrepancies between the actual utilization rate and

the desired utilization rate.

π =µ

(1 + µ)(13)

I = h.Y (14)

∆h =

h−1.γ.(u− un), if |u− un|> x

0, otherwise(15)

Since we agree with Sraffian and Classical authors when they say that the utiliza-

tion rate cannot be “anywhere” in the long run, but also agree with the neo-Kaleckians

when they point that there is no reason for firms to choose a specific number for the utiliza-

13

tion rate, we believe that adopting a range, out of which the propensity to invest reacts,

is a satisfying option, as suggested by Hein et al. (2012). As highlighted by Dutt (2011),

in a world of uncertainty, firms may want to keep their investment strategy unchanged if

the capacity utilization is within a reasonable band. This corridor is represented by the

parameter x (equation 15).19

The change in the stock of capital is given by equation 16 and differs from the

flow of investment because we include capital depreciation in the model (δ). The actual

utilization rate is given by the ratio of output to full-capacity output (equation 18) and

full-capacity output (equation 17) is determined by the ratio of the initial capital stock

to the given capital-output ratio (v). From these equations, we can draw the actual rate

of growth of the capital stock (equation 19).

K = K−1 − δK−1 + I (16)

Yfc =K−1

v(17)

u =Y

Yfc

(18)

gk =hu

v− δ (19)

Firms must still decide how they will finance their investment. We suppose firms finance

their investment through retained earnings, equity issuance and bank loans, which are

assumed to clear firms’ demand for funds (equation 20).20 Equities are a fixed proportion

(a) of the capital stock at the beginning of the period (equation 21). Firms retain a

fraction of their profit (sf ) discounting the payment of interest on loans (equation 22)

and distribute the rest of net profit to households in the form of dividends (equation 23).

Total net profit is the sum of retained and distributed profits (equation 24). Gross profit

is given by equation 25.

L = L−1 + I − FU − pe.∆E (20)

E = a.K−1 (21)

19From equation 15, we observe that, for a given adjustment parameter γ, any element that influencesthe utilization rate (see equation 29), when the latter is out of the inertia zone, will influence the short-runpropensity to invest in a pretty standard way. It will increase, for instance, in household propensities to(respectively) consume and spend, as it will decrease (given the Kaleckian features of our model) in theprofit share.

20As in many SFC models (see Lavoie and Godley (2001); Godley and Lavoie (2007); Zezza (2008)), wepresent firms’ loans as the buffer of the sector, considering, as a matter of simplification, that firms exhausttheir internal funds before recurring to external funding for investment. However, this simplification isnot suitable for analysing firms’ process of accumulating debt and their likelihood of becoming morefragile.

14

FU = sf (π.Y − irL−1) (22)

FD = (1− sf )(π.Y − ir.L−1) (23)

F = π.Y − ir.L−1 (24)

Fg = πY (25)

Normalizing equation 24 by the stock of capital at the beginning of the period, we get

what we can call a net profit rate (equation 26). Gross profit rate (equation 27) is attained

through the same procedure for equation 25.

rn = πu

v− ir

l−1

(1 + gk−1)

(26)

rg = πu

v(27)

After presenting the framework of the model, we can move on to the short run goods

market equilibrium and to the dynamic equations of the system.

3.2 Short-run goods market equilibrium

In our closed economic system, real output is the sum of household consumption,

firms investment and government expenditures (equation 28). If we substitute equations

7, 14 and 2 in equation 28, normalize it by the opening stock of capital and make some

algebraical rearrangements, we get the short run equilibrium utilization rate (equation

29). The term α2vh−1, which represents the normalized consumption out of wealth or

capitalist consumption, is the truly autonomous expenditure component of this system

(the z component). The supermultiplier appears on the RHS of equation 29 within the

parenthesis and shows the effect of induced consumption, induced investment and govern-

ment expenditures on the level of output. The essence of the supermultiplier approach is

maintained as the level of output and the utilization rate in the short run are determined

by an autonomous component of demand, which is not private business investment, times

the supermultiplier (see Freitas and Serrano, 2015).

Y = C + I +G (28)

u∗ =

(

1

(1 + gk−1)[1− h− α1(1− τ)(1− π)]− σ

)

α2vh−1v (29)

Assuming, as in neo-Kaleckian models, that the model presents Keynesian stability,

savings should react more than investment to changes in output and capacity, which

15

means that for the denominator of equation 29 to be positive the following condition

should be satisfied:

1− α1(1− τ)(1− π)−σ

(1 + gk−1)

> h (30)

3.3 Dynamic equations and Steady State ratios

We can now obtain the dynamic equations of government debt, household wealth and

firms’ loans normalized by the capital stock 21 at the beginning of the period. This step

is important in order to give us the long run equilibrium ratios, or the steady growth

ratios of the stocks. Dividing equation 1 by the lagged capital stock and making some

algebraic manipulation, we get the normalized stock of government debt (equation 31).

We can notice that the stock of government debt, in the short run, depends positively on

the stock of debt at the beginning of the period and on the after-tax interest rate (which

remunerates bills held by households). It also depends positively on the government

propensity to spend and on the profit share, since retained profits are not taxed. On

the other hand, the taxation of distributed profits, firms’ normalized stock of loans at

the beginning of the period and the capital accumulation rate have a negative effect on

government debt to capital ratio. The current capital utilization rate also has a negative

on the normalized stock of government debt, considering that the taxation of distributed

profits assumes positive values (τ(1 − sfπ)). The intuition is that since in the short run

government expenditures depend on past income, past capacity utilization should have a

positive effect on government debt to capital ratio but not the current capacity utilization,

which increases government revenues.22

bt =b−1[1 + ir(1− τ)] + σu−1 − τirsf l−1

(1 + gk−1)

− τ(1− sfπ)u

v(31)

The same procedure is applied to firms’ loans. We divide equation 20 by the lagged capital

stock and get equation 32. Firms’ loans to capital ratio depends positively on the loans

at the beginning of the period, on the interest rates they pay on this initial stock and on

the propensity to invest. As long as the propensity to invest is larger than the retained

earnings share, the effect of capacity utilization will also be positive. Firms’ loans relate

negatively to retained profits and to the capital accumulation rate. If the growth rate

21The normalized stocks of government and firms’ debt will also be referred to respectively as govern-ment bills to capital ratio and firms’ loans to capital ratio, since bills and loans are the sole componentsof these institutional sectors’ debts.

22The effects presented here are drawn based on reasonable and positive values for the parameters,as well as on the assumption that the model presents Keynesian stability and that the steady growthratios converge to a stable equilibrium, which requires as a necessary condition for the denominator ofthe equilibrium ratios to be positive.

16

assumes positive values, which is the case in normal times, the portion of wealth in the

form of equities exerts a negative impact over firms’ loans.

lt =(1 + sf ir)l−1 + λvh

1 + gk−1

+ (h− sfπ)u

v− λvh (32)

When it comes to the normalized stock of household wealth, the algebra gets slightly more

complicated. The normalized stock of wealth (equation 33) is obtained by the division

of equation 11 by the lagged capital stock. The short run stock of wealth is positively

affected by the stock of wealth at the beginning of the period, by the after-tax dividend

income, by the after-tax savings out of wages, by the interest households receive over the

stock of government bills and by the amount of interest firms pay on loans (which is the

same they receive on deposits). The normalized stock of wealth negatively relates to the

consumed portion of wealth at the beginning of the period and to the consumed portion

of after-tax wages. The equities share on wealth has an ambiguous and transient effect,

since its effects vanish in the long run. The effect of the capital accumulation rate on the

normalized stock of wealth depends on the value of the parameters of the model.

vh =(1− α2 − λ)vh

−1 + (1− τ)[(1− α1 + π(α1 − sf ))

u

v(1 + gk

−1) + sf irl−1 + irb−1]

1 + gk−1 − λ

(33)

As we are testing whether the supermultiplier results hold in a more complex economic

system, we have to deal with long run equilibrium normalized stocks, in which all growth

rates follow the growth rate of the autonomous expenditure component (34) and in which

the utilization rate converges to the normal utilization rate, or gets into the inertia zone

(35).

g∗ = gk = gvh = gb = gl (34)

u∗ ≃ un (35)

Given conditions 34 and 35, and thus considering that all stocks grow at the same rate,

normalized stocks at the beginning of the period equal normalized stocks at the end of

the period (thus ∆bt = 0) in the long run. The normalized government debt (31) can be

rewritten as:

b∗ =[σ − τ(1− sfπ)(1 + g∗)]

un

v− τirsf l

∗

g∗ − ir(1− τ)(31A)

We notice that, cet.par., an increase in the propensity to spend of the government (σ)

increases the steady state value of the debt to capital ratio. The same is true for the profit

share (π). While the firms’ loans steady state ratio affects negatively the government debt

17

- which means that when the government diminishes its debt, firms increase their leverage

-, the normal utilization level has a positive effect on the government debt ratio, as long

as the term between brackets – [σ−τ(1−sfπ)(1+g∗)] – is greater than zero. We consider

this is the case, assuming as an stylized fact that both government and firms’ debt are

positive.

Following the same steps for firms, we arrive at the long run normalized stock of loans:

l∗ =(1 + g∗)[(h− sfπ)

un

v]− gkλvh

g∗ − sf ir(32A)

In the steady state, as in the short run, firms need less borrowed funds to finance the

same amount of investment, the larger the proportion of household wealth (λ) allocated

in equities. The opposite happens with the utilization rate, cet.par., a higher normal

utilization rate implies a larger ratio of loans. The greater the propensity to invest and

the smaller the profit share, the greater will be the firms loans to capital ratio in the long

run.

The equilibrium stock of household wealth-to-capital ratio (from equation 33) is neg-

atively influenced by the propensity to consume out of wealth (α2) and by the propensity

to consume out of after-tax wages (α1). The higher is firms’ debt ratio, the higher will

be the wealth ratio, because of the higher financial income received by households, which

will also increase with the interest rate on bills and deposits. The same applies to the

government debt ratio. Other things equal, higher values for the normal utilization rate

and for the profit share also translate into a higher steady state ratio of wealth. As in

the short run, the effect of the growth rate on the steady state ratio of wealth depends

on the combination of the parameters of the model.

v∗h =(1− τ)[(1− α1 + π(α1 − sf ))

un

v(1 + gk) + irb+ sf irl]

gk + α2

(33A)

Solving equation 29 for equilibrium values, considering that conditions 34 and 35 are

satisfied and, consequently, ∆h = 0, we come to the equation for the long run growth rate

of this economy:

g∗ =α2vhv + unσ

un[1− h− α1(1− τ)(1− π)]− 1 (36)

In equation 36, we can observe that income distribution (π) as well as the other compo-

nents of the supermultiplier – propensity to invest (h), propensities to consume (α1, α2)

and propensity to spend of the government (σ) – can have permanent effects on growth.

Accordingly, the normalized consumption out of wealth also influences the rate of growth

18

Table 6: Effects of the shocks

Reduction in µ(π) Increase in α1 Increase in α2

Short run Long run Short run Long run Short run Long rung + + + + + +u + = + = + =rg − − + = + =rn − − + − + −

(α2vh).

After presenting the level and the dynamic equations and the short and long run

equilibrium conditions, we can move on to the simulation experiments to test for the long

run effects of the model.

4 Experiments

From the steady growth state, we run some simulation experiments to evaluate the

long run features of the model. The first shock is a decrease in the mark-up, which means

an increase in the wage share, in order to assess whether the paradox of costs holds in

terms of level and growth effects, considering the initial values and parameters of the

model.23 The second shock is an increase in the propensity to consume out of after-tax

wages (α1) (a reduction in the propensity to save) in order to assess whether the paradox

of thrift holds in terms of level and growth effects. At last, we shock the autonomous

consumption component, through an increase in the propensity to consume out of wealth

(α2), to analyze how it changes the dynamics of the economy in the long run. The results

of the shocks are summarized in table 6.24

4.1 The paradox of costs

A decrease in the mark-up raises the wage share and leads to a higher consumption

out of wages, which translates into a higher income and activity level. The increase in

capacity utilization following the increase in consumption and income makes firms change

their expectation of growth, which raises their propensity to invest, increasing the rate

of capital accumulation as we can see in figure 1(a). We also observe that as the rate of

growth of household wealth during the transition is lower than the capital accumulation

23The parameters and long run values of the variables are presented in table 7 in Appendix A.24All numerical simulations were computed using R and Eviews 9 software. The programming codes

of the simulations are available upon request.

19

rate (figure 1a), the ratio of household wealth to capital will be lower in comparison

to the baseline (figure 2a). As in the original supermultiplier model (Serrano, 1995a),

as investment increases in relation to output, through a higher propensity to invest h

(figure 1c), the autonomous expenditure component (consumption out of wealth) z loses

relative weight on output (figure 1d). From figure 1(b), we note that the utilization

rate converges towards the desired rate in the long run, through the adjustment of the

propensity to invest.

From equations 31 and 31A, we know that the reduction in the profit share contributes

directly to reduce government debt ratio. Besides that, a reduction in the normalized stock

of bills contributes to reduce itself further since the amount of interest the government

pays on bills (to households) also decreases. The increase in the utilization rate following

the boost in activity at the same time raises the ratio of bills to capital (since government

spends a constant fraction of output) and has a negative effect on that ratio through the

increase on taxes (figure 2a). In the short run, the government budget deficit falls sharply

but as output increases it stabilizes at a higher level compared to the baseline (figure 2c).

The increase in firms loans and the higher accumulation rate also contribute to reduce

the government bills to capital ratio.

In the case of firms, the higher loans to capital ratio is due to the increase in the

propensity to invest along with the lower amount of wealth to capital which reduces total

equities as a source of finance in comparison to the baseline (figure 2d). These effects

compensate the impact of a higher accumulation rate in reducing firms loans - through

the increase in profit income (figure 2a).

Household wealth to capital ratio is negatively influenced by the initial reduction in

the profit share, which diminishes the financial income accruing from firms’ dividends

and diminishes the immediate need for the government to issue bills since taxation from

household wage income increases. This more than compensates the effect of the increase

in the interest payments households receive from deposits (figure 1a). The growth rate of

wealth is higher in comparison to the baseline due to the overall increase in income and

activity following the higher wage share (figure 2a).

Regarding the gross and net profit rates of firms (figure 2b), it is clear that since the

utilization rate converges to a desired rate or range, both rates decrease in relation to the

baseline. In the short run, the positive effect of an increase in income and utilization is

not enough to compensate the reduction of firms profit share. However, gross and net

profit levels increase in relation to the baseline 25.

25One could say that, as firms have more than one goal in the long run, they may be willing to cut profitrates in order to grow and to increase their market shares (Lavoie, 2014).As pointed by one of anonymous

20

Based on these results, we realize that income distribution can influence growth in

the long run, even if the utilization rate converges to the desired rate or range. This is

made possible by the inclusion of the endogenous autonomous expenditure component

in the model, which means that there are factors other than the utilization rate through

which income distribution can affect output growth. Yet the profit rate cannot increase

in the long run, since the profit share decreases and the utilization rate goes back to its

normal range. In this case, even if the model only presents the paradox of costs in terms

of level effects, it is still possible to say that income distribution has a permanent impact

on growth in the long run.

4.2 The paradox of thrift

Following an increase in the propensity to consume out of wages (α1), consumption

increases and leads to an increase on output and capacity utilization. This leads to

an increase in the propensity to invest of firms and in the capital accumulation rate

(figures 3a,4c). Consumption out of wealth loses participation in income (figure 4d), with

capital accumulation growing faster than wealth, as in the first simulation experiment.

The difference here is that in the short run, the reduction in workers’ propensity to

save impacts negatively households savings and, consequently, their wealth (figure 3a).

However, as soon as consumption affects activity, the higher income will raise the financial

income received by households, which contributes positively to wealth growth.

The government debt to capital ratio also decreases as household income - due to an

increase in dividend payment and wages -, taxation and capital accumulation increase.

In the short run, as firms’ loans ratio decreases, the debt ratio falls at a slower pace. In

the long run, the reduction in the payment of interest to households, due to the lower

debt ratio, and the higher accumulation rate together with a higher loans to capital ratio

make the debt to capital ratio decrease even further (figures 3a, 3c).

Differently from the previous experiment, in this case, firms’ loans to capital ratio

falls in the short run and stabilizes at a higher ratio in the long run in comparison to the

baseline. As firms slowly increase their propensity to invest as a reaction to the higher

level of activity, the sharp increase in the accumulation rate negatively impacts the loans

to capital ratio, compensating the increase in the propensity to invest and the decrease in

the amount of equities due to the lower ratio of household wealth to capital (figures 3a,

4a, 4c). Still, in the long run, since the accumulation rate converges towards the growth

referees, the results regarding the rate of profit could also be related to a fallacy of composition betweenthe decisions of firms at the micro level and aggregate macro results. For more on this, see Hein and VanTreeck (2008).

21

Figure 1: Effects of an increase in real wages (reduction in µ)

(a) Growth rates of capital and household wealth

0.020

0.021

0.022

0.023

0.024

2000 2100 2200 2300 2400 2500

gk gvh

(b) Capacity utilization rate

0.80

0.81

0.82

0.83

0.84

0.85

2000 2100 2200 2300 2400 2500

u baseline u scenario 1

(c) Firms propensity to invest

0.200

0.205

0.210

2000 2100 2200 2300 2400 2500

h baseline h scenario 1

(d) Autonomous expenditure component to income

0.145

0.150

0.155

0.160

0.165

0.170

2000 2100 2200 2300 2400 2500

z baseline z scenario 1

22

Figure 2: Effects of an increase in real wages (reduction in µ)

(a) Steady growth state ratios

0.4

0.8

1.2

1.6

2000 2100 2200 2300 2400 2500

Bills Loans Wealth

(b) Profit rates

0.900

0.925

0.950

0.975

1.000

2000 2100 2200 2300 2400 2500

Gross profit to baseline Net profit to baseline

(c) Government budget deficit

−0.012

−0.008

−0.004

0.000

0.004

2000 2100 2200 2300 2400 2500

Govt. deficit scenario 1 Govt. deficit baseline

(d) Amount of equities

0.90

0.95

1.00

2000 2100 2200 2300 2400 2500

Amount of equities to baseline

23

rate of wealth, stabilizing at lower position in comparison to the initial shock (higher than

the baseline), the value it assumes is not enough to cover the effects of the propensity to

invest and of the amount of equities on the loans to capital ratio.

Household wealth to capital suffers the negative impact of the lower normalized stock

of government bills, since interest payments decrease, and also the negative impact of the

lower interests on deposits, as a result of lower firms’ loans ratio. However, as income and

capacity utilization increase, they have a positive effect on wealth, even if wealth grows at

a lower rate than capital accumulation. In addition to this, in the long run, as firms’ loans

attain a higher position in comparison to the baseline, they positively influence wealth

(figures 3a, 4b).

Gross and net profit rates increase in relation to their baseline values due to the

temporary increase in the utilization rate. As the utilization rate converges to its desired

level, and there are no changes in the profit share, the gross profit rate goes back to

its baseline value. The net profit rate decreases as the ratio of loans to capital rests at

a higher level, which means that a larger part of profits is destined to the payment of

interest on loans (figure 3d).

In sum, we observe that the paradox of thrift in terms of growth effects is still valid in

the long run in this framework in which there is an autonomous expenditure component

working as an “attractor” to growth and with the utilization rate converging to a de-

sired range. This happens because the reduction in the propensity to save stimulates the

economy, boosting consumption from wages, which entails both a higher output level in

relation to the baseline, and a higher growth rate in the long run, through the supermul-

tiplier. Differently from neo-Kaleckian models, in which the effect happens through the

utilization rate, raising the level of activity and the accumulation rate, in this model the

effect happens through the utilization rate in the short run; however, the accumulation

rate depends on the output, which ultimately depends on the autonomous expenditure

component (consumption out of wealth) and on its multiplier which is permanently in-

creased, raising the overall rate of growth of the economy.

4.3 A shock to the propensity to consume out of wealth

An increase in the propensity to consume out of wealth increases consumption, which

reduces household savings and, consequently, household wealth in the short run. Dif-

ferently from the previous experiment, the autonomous component of demand increases

relatively to income, but as soon as the effect on capacity kicks in, consumption out of

wealth decreases in relation to output (figure 5d). As in earlier experiments, the higher

24

Figure 3: Effects of an increase in the propensity to consume out of income (α1)

(a) Growth rates of capital and household wealth

0.018

0.020

0.022

0.024

2000 2100 2200 2300 2400 2500

gk gvh

(b) Capacity utilization rate

0.80

0.82

0.84

2000 2100 2200 2300 2400 2500

u baseline u scenario 2

(c) Steady growth state ratios

0.50

0.75

1.00

1.25

1.50

2000 2100 2200 2300 2400 2500

Bills Loans Wealth

(d) Profit rates

1.00

1.02

1.04

1.06

1.08

2000 2100 2200 2300 2400 2500

Gross profit to baseline Net profit to baseline

25

Figure 4: Effects of an increase in the propensity to consume out of income (α1)

(a) Firms loans ratio

0.750

0.775

0.800

0.825

2000 2100 2200 2300 2400 2500

Baseline Firms loans

(b) Househould wealth to capital ratio

1.45

1.50

1.55

1.60

1.65

2000 2100 2200 2300 2400 2500

Baseline Household wealth

(c) Propensity to invest

0.2000

0.2025

0.2050

0.2075

2000 2100 2200 2300 2400 2500

h baseline h scenario 2

(d) Autonomous expenditure component to income

0.150

0.155

0.160

0.165

0.170

2000 2100 2200 2300 2400 2500

z baseline z scenario 2

26

Figure 5: Effects of an increase in the autonomous expenditure component (increase inα2)

(a) Growth rates of capital and household wealth

0.018

0.020

0.022

0.024

2000 2100 2200 2300 2400 2500

gk gvh

(b) Capacity utilization rate

0.80

0.82

0.84

0.86

2000 2100 2200 2300 2400 2500

u baseline u scenario 3

(c) Firms propensity to invest

0.2000

0.2025

0.2050

0.2075

0.2100

2000 2100 2200 2300 2400 2500

h baseline h scenario 3

(d) Autonomous expenditure component to income

0.165

0.170

0.175

0.180

2000 2100 2200 2300 2400 2500

z baseline z scenario 3

utilization rate (figure 5b) leads firms to increase their propensity to invest, which in-

creases the accumulation rate at a faster pace than that of household wealth (figures 5a,

5c). The effects on the ratios of government bills to capital, firms loans to capital and

household wealth to capital are very similar to the effects of a shock in the propensity to

consume out of wages. Government bills and household wealth to capital ratios stabilize

at lower positions in comparison to the baseline, while the firms loans ratio decreases in

the short run but increases in the long run. The gross profit rate increases in the short

run but goes back to its baseline rate while the net profit rate decreases as the amount

of interest payment on loans increases in the long run.

27

4.4 An assessment of the shocks

All the scenarios have in common the fact that changes in exogenous parameters alter

(directly or indirectly) the supermultiplier, and thus affect the long run growth rate as

well. Therefore, as long as the autonomous expenditure component is endogenous to

the model, the effects of the shocks are not restricted to the transition period. The

experiments then show that while the utilization converges back to its desired level or

range, the adjustments of a shock to income distribution or to the propensity to save can

be absorbed through an endogenous change in the growth rate. It is worth mentioning

that this happens without the loss of the Keynesian causality, since the adjustment of

capacity to demand occurs through changes in the autonomous component of demand,

whose share in income falls when investment rises.

It goes without saying that most of the results of our experiments were only made

possible by the adoption of an SFC framework. In the original supermultiplier approach,

autonomous demand growth is given once and for all – or until it is exogenously changed.

This exogeneity makes it impossible to establish the connections between a change in

the propensity to invest and the determinants of the autonomous expenditure (household

wealth, in the case of this paper). Moreover, the omission of financial variables prevents

the evaluation of the effects of an increase in capital accumulation and in the autonomous

expenditure growth rate on the financial stocks of the economy (loans, bills, household

wealth). It also prevents understanding that a permanent (say) increase in the supermul-

tiplier allows for a permanent increase in the growth rate of wealth in the same direction

despite the reduction of the household wealth to capital ratio.

5 Final remarks

As we have seen, so far supermultiplier models do not deal properly with financial

issues. They do not take into consideration the interactions between financial stocks and

flows and how such interactions could impact growth in the long run. Since the growth

rate of the autonomous expenditure component is exogenously given, these models do not

allow for the emergence of the paradoxes of thrift and costs in terms of growth effects. It

does not matter which “non capacity creating” autonomous expenditure is leading growth

in the long run, whether consumption, government expenditures, or net exports, only the

level effects of changes in income distribution and in the propensity to save will last.

However, when we allow for the autonomous expenditure component to be endogenous,

as in the model we built here, which depends on household wealth, we also allow for

28

feedbacks between financial income and financial stocks, as for feedbacks between the

latter and the capital stock. Changes in income distribution and in the propensity to save

will permanently affect the growth rate of the economy, through the supermultiplier, and

through the dynamics of household wealth to capital ratio.

The main results obtained through the experiments of section 4 can be summarized

as follows:

(i) An essential claim of the Supermultiplier approach is that a higher growth rate

of the autonomous expenditure component is associated with a higher investment

to income ratio. This assumption still holds for a more complex model even if

the autonomous expenditure component is endogenous to the economic system.

As the autonomous expenditure component grows at a faster pace it increases the

income which will stimulate more expenditures, say by increasing consumption out

of wages, and these higher expenditures will boost investment, as the utilization

of capacity rises. As investment accelerates induced by income, the investment

share increases relatively to income while the reverse happens to the autonomous

expenditure component share (Serrano, 1995b);

(ii) The paradox of costs is still valid in terms of level effects. A reduction in the

mark-up of firms (lower profit share) leads to lower profit rate, but to a higher

level of profits in the long run, as a consequence of the higher capital accumulation.

However, differently from other supermultiplier models, a higher wage share has a

permanent growth effect, through the supermultiplier mechanism. The discrepancy

between actual and desired utilization rates promotes a permanent increase in the

propensity to invest. This, along with the higher wage share, compensates the effect

of a lower wealth-to-capital ratio on the growth rate of this economy;

(iii) The paradox of thrift is valid both in level and in growth terms in the long run. An

increase in the propensity to consume out of after-tax wages permanently affects

the growth rate of the economy in the long run through the supermultiplier;

(iv) The relation between stocks and flows matter, since an increase in the propensity to

invest contributes to increase the stock of firms’ debt to capital. This implies that

the propensity to invest can find a constraint in the values it can assume, coming

from the amount of loans firms borrow in order to finance this same investment and

which also depends on the how the propensity to invest will impact the accumulation

rate, in order to compensate the higher loans-to-capital ratio;

(v) The behaviour of the autonomous component reveals once more the centrality of

29

stock and flow interactions, for consumption out of wealth is influenced by the gov-

ernment debt ratio, by firms’ propensity to invest and by the capital accumulation

rate;

Needless to say, the discussion presented here could be enriched in several ways. The

first one concerns the generality of our conclusions, which should be evaluated by means

of a stability analysis of the model and a sensitivity analysis of the parameters to verify

for which range of (economically meaningful) parameters the paradoxes remain valid in

the long run. Second, it would be important to move to an open economy setting; it is

well known that the paradox of costs may not hold when international transactions are

taken into account. Third, it would also be important to test the same hypothesis for

an economy with a more complex financial system, for instance incorporating consumer

credit and assuming a more ”active” and profit-earning banking sector, including the

possibility of credit rationing.

A final and possibly important front which would require further research refers to the

implication of specific growth engines. There is no reason to assume that a consumption-

led growth regime will be as durable as (say) a government- or an export-led one. Each

growth engine will feature specific interactions between stocks and flows, will face specific

financial constraints and will present different stability conditions.

References

Allain, O. (2014). Macroeconomic effects of consumer debt: three theoretical essays. In18th FMM conference on the inequality and the future of capitalism, Berlin.

Allain, O. (2015a). Demographic Growth , Harrodian ( In ) Stability and the Supermul-tiplier * Demographic Growth , Harrodian ( In ) Stability and the Supermultiplier. In19th FMM Conference, pages 1–23.

Allain, O. (2015b). Tackling the instability of growth: a Kaleckian-Harrodian model withan autonomous expenditure component. Cambridge Journal of Economics, 39(5):1351–1371.

Amadeo, E. (1986). Notes on capacity utilization, distribution and accumulation. Con-

tributions to Political Economy, 5(1, March):83–94.

Amadeo, E. (1987). Expectations in a Steady-State Model of Capacity Utilization. Po-

litical Economy: studies in the Surplus Approach, 3(1):75–89.

Barba, a. and Pivetti, M. (2008). Rising household debt: Its causes and macroeconomicimplications–a long-period analysis. Cambridge Journal of Economics, 33(1):113–137.

30

Bhaduri, A. and Marglin, S. (1990). Unemployment and the real wage: the economicbasis for contesting political ideologies. Cambridge Journal of Economic, 14:375–393.

Bibow, J. (2010). Financialization of the U.S. household sector: the ”subprime mortgagecrisis” in the U.S. and global perspective. In Study 3, Study, Dusseldorf. IMK.

Blecker, R. a. (2009). Long-run growth in open economies: export-led cumulative cau-sation or a balance-of-payments constraint? In 2nd Summer School on “Keynesian

Macroeconomics and European Economic Policies”, page 36, Berlin.

Bortis, H. (1997). Institutions, Behaviour and Economic Theory: A contribution to

Classical-Keynesian Political Economy. Cambridge University Press, Cambridge.

Bortz, P. G. (2014). Foreign debt, distribution, inflation and growth in a SFC model.European Journal of Economics and Economic Policies: Intervention, 11(3):269–299.

Brown, C. (2007). Financial engineering, consumer credit, and the stability of effectivedemand. Journal of Post Keynesian Economics, 29(3):427–450.

Cesaratto, S. (2015). Neo-Kaleckian and Sraffian Controversies on the Theory of Accu-mulation. Review of Political Economy, 27(2):154–182.

Cesaratto, S., Serrano, F., and Stirati, A. (2003). Technical Change, Effective Demandand Employment. Review of Political Economy, 15(1):33–52.

Cynamon, B. Z. and Fazzari, S. M. (2008). Household Debt in the Consumer Age : Sourceof Growth — Risk of Collapse Household Debt in the Consumer Age : Source of Growth— Risk of Collapse. Capitalism and Society, 3(2).

Dejuan, O. (2014). How to escape from the trap of the warranted rate of growth. pages1–21.

Dos Santos, C. H. and Zezza, G. (2008). a Simplified, ‘Benchmark’, Stock-Flow ConsistentPost-Keynesian Growth Model. Metroeconomica, 59(3):441–478.

Dutt, A. K. (1984). Stagnation, income distribution and monopoly power. Cambridge

Journal of Economics, 8(1, March):25–40.

Dutt, A. K. (2011). Growth and income distribution: a post-Keynesian perspective. InHein, E. and Stockhammer, E., editors, A modern guide to Keynesian macroeconomics

and Economic Policies, pages 61–87. E. Elgar, Cheltenham, UK and Northampton,MA, USA.

Dutt, A. K. (2015). Growth and Distribution with Exogenous Autonomous DemandGrowth and Normal Capacity Utilization.

Dutt, A. K. (2016). Autonomous Demand Growth and Government Debt in the shortrun.

Fazzari, S. M., Ferri, P. E., Greenberg, E. G., and Variato, A. M. (2013). Aggregatedemand, instability, and growth. Review of Keynesian Economics, 1(1):1–21.

31

Fiebiger, B. and Lavoie, M. (2016). Trade and Business Cycles with External Markets?Non-Capacity Generating Semi-Autonomous Expneditures and Effective Demand.

Freitas, F. and Serrano, F. (2015). Growth Rate and Level Effects , the Stability ofthe Adjustment of Capacity to Demand and the Sraffian Supermultiplier. Review of

Political Economy, 27(3):258–281.

Girardi, D. and Pariboni, R. (2015). Autonomous demand and economic growth : someempirical evidence.

Godley, W. and Lavoie, M. (2007). Monetary Economics An Integrated Approach to

Credit, Money, Income, Production and Wealth, volume 12.

Guttmann, R. and Plihon, D. (2008). O endividamento do consumidor no cerne docapitalismo conduzido pelas financas. Economia e Sociedade, 17(numero especial):575–610.

Harrod, R. F. (1939). An essay in dynamic theory. Economic Journal, 49(193):14–33.

Hein, E. (2016). Autonomous government expenditure growth, deficits, debt and distri-bution in a neo-Kaleckian growth model.

Hein, E., Lavoie, M., and van Treeck, T. (2011). Some instability puzzles in Kaleckianmodels of growth and distribution: A critical survey. Cambridge Journal of Economics,35(3):587–612.

Hein, E., Lavoie, M., and Van Treeck, T. (2012). Harrodian Instability and the ’NormalRate’ of Capacity Utilization in Kaleckian Models of Distribution and Growth - asurvey. Metroeconomica, 63(1):139–169.

Hein, E. and Van Treeck, T. (2008). ’Financialisation’ in Post-Keynesian models of dis-tribution and growth - systematic review.

Kaldor, N. (1961). Capital accumulation and economic growth. In The Theory of Capital,pages 177–228. St. Martin’s Press, New York.

Kalecki, M. (1969). Studies in the Theory of Business Cycles 1933-1939. Basil Blackwell,Oxford.

Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. Macmil-lan, London.

Kregel, J. a. (1980). Economic Dynamics and the Theory of Steady Growth: An HistoricalEssay on Harrod’s ’Knife-edge’. History of Political Economy, 12(1):97–123.

Lavoie, M. (2006). Do heterodox theories have anything in common? A post-Keynesianpoint of view. Intervention. European Journal of Economics and Economic Policies,3(1):87–112.

Lavoie, M. (2010). Should Sraffian economics be dropped out of the post-Keynesianschool? In Sraffa’s Production of Commodities 1960-2010, Critique and reconstruction

of economic theory at Roma Tre, pages 1–31, Roma.

32

Lavoie, M. (2014). Post-Keynesian Economics: New Foundations.

Lavoie, M. (2016). Convergence towards the normal rate of capacity utilization in neo-kaleckian models: The role of non-capacity creating autonomous expenditures. Metroe-

conomica, 67(1):172–201.

Lavoie, M. and Godley, W. (2001). Kaleckian models of growth in a coherent stock-flow monetary framework: a Kaldorian view. Journal of Post Keynesian Economics,24(2):277–311.

Le Heron, E. and Mouakil, T. (2008). A Post-Keynesian Stock-Flow Consistent Model forDynamic Analysis of Monetary Policy Shock on Banking Behaviour. Metroeconomica,59(3):405–440.

Leite, F. P. (2015). Taking Godley’s Ratios Seriously. Metroeconomica, 66(3):508–533.

Nah, W. J. and Lavoie, M. (2017). Long run Convergence in a Neo-Kaleckian Open-economy Model with Autonomous Export Growth. Journal of Post Keynesian Eco-

nomics, (February).

Pedrosa, I. and Macedo e Silva, A. C. (2014). A Minskyan-Fisherian SFC model foranalyzing the linkages of private financial behavior and public debt. In 18th FMM

conference on the inequality and the future of capitalism, Berlin.

Robinson, J. (1962). Essays in the theory of economic growth. Joan Robinson Series.Macmillan, London.

Rowthorn, B. (1981). Demand, real wages and economic growth. Thames Papers in

Political Economy, Autumn:1–39.

Ryoo, S. and Skott, P. (2013). Public Debt and Full Employment in a Stock-Flow Consis-tent Model of a Corporate Economy. Journal of Post Keynesian Economics, 35(4):511–528.

Serrano, F. (1995a). Long period effective demand and the sraffian supermultiplier. Con-tributions to Political Economy, 14:67–90.

Serrano, F. (1995b). The Sraffian Multiplier. Phd dissertation, University of Cambridge.

Skott, P. (2010). Growth, instability and cycles: Harrodian and Kaleckian models of accu-mulation and income distribution. In Setter, editor, Handbook of Alternative Theories

of Economic Growth2, pages 108–31. E. Elgar, Cheltenham, UK and Northampton,MA, USA.

White, G. (2008). Growth, Autonomous Demand and a Joint-product Treatment of FixedCapital. Metroeconomica, 59(1):1–26.

Zezza, G. (2008). US growth, the housing market, and the distribution of income. Journalof Post Keynesian Economics, 30(3):375–401.

33

Appendix A

Table 7: Parameters and long run value of variables

Parameters/variables Baseline Scenario 1 Scenario 2 Scenario 3

τ 0.37 0.37 0.37 0.37σ 0.34 0.34 0.34 0.34α1 0.8 0.8 0.84 0.8α2 0.03373529 0.03373529 0.03373529 0.0374a 0.1 0.1 0.1 0.1x 0.001 0.001 0.001 0.001λ0 0.08 0.08 0.08 0.08pe 0.9880216 0.8493563 0.8571246 0.846402δ 0.044 0.044 0.044 0.044ir 0.02 0.02 0.02 0.02v 2.5 2.5 2.5 2.5µ 0.7 0.63 0.7 0.7π 0.4117647 0.3865031 0.4117647 0.4117647sf 0.4 0.4 0.4 0.4γ 0.014 0.014 0.014 0.014h 0.2 0.2131375 0.2091036 0.2101661

u ≃ un 0.8 0.8 0.8 0.8m∗ = l∗ 0.7953297 1.054224 0.840638 0.8442299

b∗ 0.7525708 0.276434 0.5021906 0.4817999v∗h 1.646703 1.415594 1.428541 1.41067g∗ 0.02 0.02421 0.02291702 0.023161

34